Why OBJ export writes face normals instead of vertex normals
They are vertex normals. But because your cube is flat shaded, there are only 6 unique vector directions. In the obj file there are no duplicates. If you smooth shade your cube, you'll get 8 vn entries.

You can see that first face is made from vertices 1,5,7,3 and that they have normal vectors 1,1,1,1 (in same order)